{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (4, 4)\n",
    "plt.rcParams['figure.dpi'] = 150\n",
    "plt.rcParams['lines.linewidth'] = 3\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.linear_model import LogisticRegressionCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1: Using Regularization and Cross Validation to Avoid Overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we split the NBA data into a training and a test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "df = pd.read_csv(r\"data_set\\nba.csv\").sample(frac=1)\n",
    "df[\"WON\"] = df[\"WL\"]\n",
    "df[\"WON\"] = df[\"WON\"].replace(\"W\", 1)\n",
    "df[\"WON\"] = df[\"WON\"].replace(\"L\", 0)\n",
    "df_train, df_test = np.split(df, [2000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SEASON_ID</th>\n",
       "      <th>TEAM_ID</th>\n",
       "      <th>TEAM_ABBREVIATION</th>\n",
       "      <th>TEAM_NAME</th>\n",
       "      <th>GAME_ID</th>\n",
       "      <th>GAME_DATE</th>\n",
       "      <th>MATCHUP</th>\n",
       "      <th>WL</th>\n",
       "      <th>MIN</th>\n",
       "      <th>FGM</th>\n",
       "      <th>...</th>\n",
       "      <th>REB</th>\n",
       "      <th>AST</th>\n",
       "      <th>STL</th>\n",
       "      <th>BLK</th>\n",
       "      <th>TOV</th>\n",
       "      <th>PF</th>\n",
       "      <th>PTS</th>\n",
       "      <th>PLUS_MINUS</th>\n",
       "      <th>VIDEO_AVAILABLE</th>\n",
       "      <th>WON</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>234</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612754</td>\n",
       "      <td>IND</td>\n",
       "      <td>Indiana Pacers</td>\n",
       "      <td>21800120</td>\n",
       "      <td>2018-11-02</td>\n",
       "      <td>IND @ CHI</td>\n",
       "      <td>W</td>\n",
       "      <td>240</td>\n",
       "      <td>40</td>\n",
       "      <td>...</td>\n",
       "      <td>42</td>\n",
       "      <td>21</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "      <td>13</td>\n",
       "      <td>107</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1395</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612753</td>\n",
       "      <td>ORL</td>\n",
       "      <td>Orlando Magic</td>\n",
       "      <td>21800695</td>\n",
       "      <td>2019-01-21</td>\n",
       "      <td>ORL @ ATL</td>\n",
       "      <td>W</td>\n",
       "      <td>240</td>\n",
       "      <td>46</td>\n",
       "      <td>...</td>\n",
       "      <td>45</td>\n",
       "      <td>29</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>11</td>\n",
       "      <td>22</td>\n",
       "      <td>122</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1410</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612759</td>\n",
       "      <td>SAS</td>\n",
       "      <td>San Antonio Spurs</td>\n",
       "      <td>21800711</td>\n",
       "      <td>2019-01-23</td>\n",
       "      <td>SAS @ PHI</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>47</td>\n",
       "      <td>...</td>\n",
       "      <td>36</td>\n",
       "      <td>24</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>120</td>\n",
       "      <td>-2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1730</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612760</td>\n",
       "      <td>OKC</td>\n",
       "      <td>Oklahoma City Thunder</td>\n",
       "      <td>21800866</td>\n",
       "      <td>2019-02-14</td>\n",
       "      <td>OKC @ NOP</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>50</td>\n",
       "      <td>...</td>\n",
       "      <td>48</td>\n",
       "      <td>27</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>21</td>\n",
       "      <td>122</td>\n",
       "      <td>-9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1307</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612760</td>\n",
       "      <td>OKC</td>\n",
       "      <td>Oklahoma City Thunder</td>\n",
       "      <td>21800653</td>\n",
       "      <td>2019-01-15</td>\n",
       "      <td>OKC @ ATL</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>43</td>\n",
       "      <td>...</td>\n",
       "      <td>40</td>\n",
       "      <td>22</td>\n",
       "      <td>16</td>\n",
       "      <td>3</td>\n",
       "      <td>12</td>\n",
       "      <td>18</td>\n",
       "      <td>126</td>\n",
       "      <td>-16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SEASON_ID     TEAM_ID TEAM_ABBREVIATION              TEAM_NAME  \\\n",
       "234       22018  1610612754               IND         Indiana Pacers   \n",
       "1395      22018  1610612753               ORL          Orlando Magic   \n",
       "1410      22018  1610612759               SAS      San Antonio Spurs   \n",
       "1730      22018  1610612760               OKC  Oklahoma City Thunder   \n",
       "1307      22018  1610612760               OKC  Oklahoma City Thunder   \n",
       "\n",
       "       GAME_ID   GAME_DATE    MATCHUP WL  MIN  FGM  ...  REB  AST  STL  BLK  \\\n",
       "234   21800120  2018-11-02  IND @ CHI  W  240   40  ...   42   21    8    9   \n",
       "1395  21800695  2019-01-21  ORL @ ATL  W  240   46  ...   45   29    8    8   \n",
       "1410  21800711  2019-01-23  SAS @ PHI  L  240   47  ...   36   24    8    6   \n",
       "1730  21800866  2019-02-14  OKC @ NOP  L  240   50  ...   48   27    8    6   \n",
       "1307  21800653  2019-01-15  OKC @ ATL  L  240   43  ...   40   22   16    3   \n",
       "\n",
       "      TOV  PF  PTS  PLUS_MINUS  VIDEO_AVAILABLE  WON  \n",
       "234    11  13  107           2                1    1  \n",
       "1395   11  22  122          19                1    1  \n",
       "1410   15  15  120          -2                1    0  \n",
       "1730   13  21  122          -9                1    0  \n",
       "1307   12  18  126         -16                1    0  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SEASON_ID</th>\n",
       "      <th>TEAM_ID</th>\n",
       "      <th>TEAM_ABBREVIATION</th>\n",
       "      <th>TEAM_NAME</th>\n",
       "      <th>GAME_ID</th>\n",
       "      <th>GAME_DATE</th>\n",
       "      <th>MATCHUP</th>\n",
       "      <th>WL</th>\n",
       "      <th>MIN</th>\n",
       "      <th>FGM</th>\n",
       "      <th>...</th>\n",
       "      <th>REB</th>\n",
       "      <th>AST</th>\n",
       "      <th>STL</th>\n",
       "      <th>BLK</th>\n",
       "      <th>TOV</th>\n",
       "      <th>PF</th>\n",
       "      <th>PTS</th>\n",
       "      <th>PLUS_MINUS</th>\n",
       "      <th>VIDEO_AVAILABLE</th>\n",
       "      <th>WON</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2036</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612751</td>\n",
       "      <td>BKN</td>\n",
       "      <td>Brooklyn Nets</td>\n",
       "      <td>21801017</td>\n",
       "      <td>2019-03-13</td>\n",
       "      <td>BKN @ OKC</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>35</td>\n",
       "      <td>...</td>\n",
       "      <td>43</td>\n",
       "      <td>19</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>96</td>\n",
       "      <td>-12</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612751</td>\n",
       "      <td>BKN</td>\n",
       "      <td>Brooklyn Nets</td>\n",
       "      <td>21800026</td>\n",
       "      <td>2018-10-20</td>\n",
       "      <td>BKN @ IND</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>41</td>\n",
       "      <td>...</td>\n",
       "      <td>40</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>20</td>\n",
       "      <td>18</td>\n",
       "      <td>112</td>\n",
       "      <td>-20</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>260</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612762</td>\n",
       "      <td>UTA</td>\n",
       "      <td>Utah Jazz</td>\n",
       "      <td>21800131</td>\n",
       "      <td>2018-11-03</td>\n",
       "      <td>UTA @ DEN</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>33</td>\n",
       "      <td>...</td>\n",
       "      <td>40</td>\n",
       "      <td>22</td>\n",
       "      <td>12</td>\n",
       "      <td>7</td>\n",
       "      <td>13</td>\n",
       "      <td>21</td>\n",
       "      <td>88</td>\n",
       "      <td>-15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2277</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612751</td>\n",
       "      <td>BKN</td>\n",
       "      <td>Brooklyn Nets</td>\n",
       "      <td>21801137</td>\n",
       "      <td>2019-03-30</td>\n",
       "      <td>BKN vs. BOS</td>\n",
       "      <td>W</td>\n",
       "      <td>240</td>\n",
       "      <td>38</td>\n",
       "      <td>...</td>\n",
       "      <td>40</td>\n",
       "      <td>22</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>17</td>\n",
       "      <td>110</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1751</th>\n",
       "      <td>22018</td>\n",
       "      <td>1610612737</td>\n",
       "      <td>ATL</td>\n",
       "      <td>Atlanta Hawks</td>\n",
       "      <td>21800877</td>\n",
       "      <td>2019-02-22</td>\n",
       "      <td>ATL vs. DET</td>\n",
       "      <td>L</td>\n",
       "      <td>240</td>\n",
       "      <td>43</td>\n",
       "      <td>...</td>\n",
       "      <td>47</td>\n",
       "      <td>21</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>18</td>\n",
       "      <td>24</td>\n",
       "      <td>122</td>\n",
       "      <td>-3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SEASON_ID     TEAM_ID TEAM_ABBREVIATION      TEAM_NAME   GAME_ID  \\\n",
       "2036      22018  1610612751               BKN  Brooklyn Nets  21801017   \n",
       "62        22018  1610612751               BKN  Brooklyn Nets  21800026   \n",
       "260       22018  1610612762               UTA      Utah Jazz  21800131   \n",
       "2277      22018  1610612751               BKN  Brooklyn Nets  21801137   \n",
       "1751      22018  1610612737               ATL  Atlanta Hawks  21800877   \n",
       "\n",
       "       GAME_DATE      MATCHUP WL  MIN  FGM  ...  REB  AST  STL  BLK  TOV  PF  \\\n",
       "2036  2019-03-13    BKN @ OKC  L  240   35  ...   43   19    7    5   17  18   \n",
       "62    2018-10-20    BKN @ IND  L  240   41  ...   40   25    6    6   20  18   \n",
       "260   2018-11-03    UTA @ DEN  L  240   33  ...   40   22   12    7   13  21   \n",
       "2277  2019-03-30  BKN vs. BOS  W  240   38  ...   40   22    7    2   14  17   \n",
       "1751  2019-02-22  ATL vs. DET  L  240   43  ...   47   21    6    4   18  24   \n",
       "\n",
       "      PTS  PLUS_MINUS  VIDEO_AVAILABLE  WON  \n",
       "2036   96         -12                1    0  \n",
       "62    112         -20                1    0  \n",
       "260    88         -15                1    0  \n",
       "2277  110          14                1    1  \n",
       "1751  122          -3                1    0  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1A: Training an Unregularized Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use all of the numerical features available to us. These are given in `p1_features` below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1_features = [\n",
    "    'FGM', 'FGA', 'FG_PCT', 'FG3M', 'FG3A', 'FG3_PCT', 'FTM', 'FTA', 'FT_PCT',\n",
    "    'OREB', 'DREB', 'REB', 'AST', 'STL', 'BLK', 'TOV', 'PF', 'PTS'\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, train an unregularized LogisticRegression model called `unregularized_model`. Your model should try to fit `df_train[\"WON\"]` from the features in `p1_features`.\n",
    "\n",
    "Make sure to set `penalty = 'none'`. Also, don't use `PolynomialFeatures`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('model',\n",
       "                 LogisticRegression(C=1.0, class_weight=None, dual=False,\n",
       "                                    fit_intercept=True, intercept_scaling=1,\n",
       "                                    l1_ratio=None, max_iter=10000,\n",
       "                                    multi_class='auto', n_jobs=None,\n",
       "                                    penalty='none', random_state=None,\n",
       "                                    solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                                    warm_start=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unregularized_model = Pipeline([('scale', StandardScaler()),\n",
    "                                ('model',\n",
    "                                 LogisticRegression(penalty='none',\n",
    "                                                    max_iter=10000))])\n",
    "unregularized_model.fit(df_train[p1_features], df_train['WON'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we compute the accuracy of your classifier on the training and test set using sklearn's built-in `accuracy_score`. You should get around 84% for the training accuracy and around 83% for the test accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.845"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(df_train[\"WON\"],\n",
    "               unregularized_model.predict(df_train[p1_features]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8304347826086956"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_test[\"WON\"],\n",
    "               unregularized_model.predict(df_test[p1_features]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00801763])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unregularized_model.named_steps['model'].intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.51677642, -3.09844068, -0.69522002,  0.29085264, -0.04164525,\n",
       "         0.16738635,  0.11752186, -0.54056489,  0.1561913 ,  0.69723721,\n",
       "         1.04930524,  1.23672583,  0.10183484,  1.18194725,  0.21482446,\n",
       "        -1.25987005, -0.18665515,  1.402673  ]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unregularized_model.named_steps['model'].coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1B: Computing the Cross Entropy Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we gave the accuracy for your model. Below, compute the average cross-entropy loss on the training and test sets. \n",
    "\n",
    "Hint: You'll need to import `log_loss`. \n",
    "\n",
    "Hint: `log_loss` needs probabilities, not classes, so make sure to use `predict_proba` instead of `predict`.\n",
    "\n",
    "You should get around 0.34 for the training set and 0.355 for the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import log_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33871656339696254"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_mean_cross_entropy_loss = log_loss(\n",
    "    df_train[\"WON\"], unregularized_model.predict_proba(df_train[p1_features]))\n",
    "training_mean_cross_entropy_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.356566085360994"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_mean_cross_entropy_loss = log_loss(\n",
    "    df_test[\"WON\"], unregularized_model.predict_proba(df_test[p1_features]))\n",
    "test_mean_cross_entropy_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Important note:** The `.fit` method in `LogisticRegression` picks parameters that minimize the log loss. It does not directly consider accuracy.\n",
    "\n",
    "We will see in optional problem 3 that sometimes these two ideas are in conflict."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1C: Training a Degree 3 Unregularized Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, train a model called `unregularized_poly3_model` that is exactly like your model from part 1A, except that it uses `PolynomialFeatures` with degree 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('poly',\n",
       "                 PolynomialFeatures(degree=3, include_bias=True,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LogisticRegression(C=1.0, class_weight=None, dual=False,\n",
       "                                    fit_intercept=True, intercept_scaling=1,\n",
       "                                    l1_ratio=None, max_iter=10000,\n",
       "                                    multi_class='auto', n_jobs=None,\n",
       "                                    penalty='none', random_state=None,\n",
       "                                    solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                                    warm_start=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unregularized_poly3_model = Pipeline([('scale', StandardScaler()),\n",
    "                                      ('poly', PolynomialFeatures(3)),\n",
    "                                      ('model',\n",
    "                                       LogisticRegression(penalty='none',\n",
    "                                                          max_iter=10000))])\n",
    "unregularized_poly3_model.fit(df_train[p1_features], df_train['WON'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compute the accuracy of your model on the training and test sets. You should get 100% accuracy training set, and around 73% on your test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_train[\"WON\"],\n",
    "               unregularized_poly3_model.predict(df_train[p1_features]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.741304347826087"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_test[\"WON\"],\n",
    "               unregularized_poly3_model.predict(df_test[p1_features]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are clearly overfitting here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1D: Regularized Model with Hard-Coded C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way to avoid overfitting is to regularize our model. Below, train a model `C1000_poly3_model` that appleis regularization with C1000. Recall, to enable regularization, simply delete `penalty = 'none'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('poly',\n",
       "                 PolynomialFeatures(degree=3, include_bias=True,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LogisticRegression(C=1000, class_weight=None, dual=False,\n",
       "                                    fit_intercept=True, intercept_scaling=1,\n",
       "                                    l1_ratio=None, max_iter=10000,\n",
       "                                    multi_class='auto', n_jobs=None,\n",
       "                                    penalty='l2', random_state=None,\n",
       "                                    solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                                    warm_start=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C1000_poly3_model = Pipeline([('scale', StandardScaler()),\n",
    "                              ('poly', PolynomialFeatures(3)),\n",
    "                              ('model',\n",
    "                               LogisticRegression(C=1000, max_iter=10000))])\n",
    "C1000_poly3_model.fit(df_train[p1_features], df_train['WON'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Give the accuracy on the training and test set below. You should see that the accuracy score is still 100% for the training set, but the test set accuracy is somewhat better at around 75.5%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_train[\"WON\"],\n",
    "               C1000_poly3_model.predict(df_train[p1_features]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7565217391304347"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_test[\"WON\"], C1000_poly3_model.predict(df_test[p1_features]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1E: Using Cross Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we selected an arbitrary C. Perhaps some other C would work better. There are two ways to find a better C:\n",
    "\n",
    "#1. Find the C that works best on a validation set.\n",
    "#2. Use cross validation.\n",
    "\n",
    "In this case, we have not kept any data aside as a validation set, so we can't do #1. So let's do #2 instead.\n",
    "\n",
    "Below train a LogisticRegressionCV model called `cv_poly3_model`, and test C values between 10^-7 and 10^5. For example, you might specify `Cs = 10**np.linspace(-7, 5, 100)`. Set `cv = 3` so that you have 3-fold cross validation.\n",
    "\n",
    "This might take a while to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('poly',\n",
       "                 PolynomialFeatures(degree=3, include_bias=True,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LogisticRegressionCV(Cs=array([1.00000000e-07, 1.32194115e-07, 1.74752840e-07, 2.31012970e-07,\n",
       "       3.05385551e-07, 4.03701726e-07, 5.33669923e-07, 7.05480231e-07,\n",
       "       9.326033...\n",
       "       1.41747416e+04, 1.87381742e+04, 2.47707636e+04, 3.27454916e+04,\n",
       "       4.32876128e+04, 5.72236766e+04, 7.56463328e+04, 1.00000000e+05]),\n",
       "                                      class_weight=None, cv=3, dual=False,\n",
       "                                      fit_intercept=True, intercept_scaling=1.0,\n",
       "                                      l1_ratios=None, max_iter=10000,\n",
       "                                      multi_class='auto', n_jobs=None,\n",
       "                                      penalty='l2', random_state=None,\n",
       "                                      refit=True, scoring=None, solver='lbfgs',\n",
       "                                      tol=0.0001, verbose=0))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_poly3_model = Pipeline([('scale', StandardScaler()),\n",
    "                           ('poly', PolynomialFeatures(3)),\n",
    "                           ('model',\n",
    "                            LogisticRegressionCV(Cs=10**np.linspace(-7, 5, 100),\n",
    "                                                 cv=3,\n",
    "                                                 max_iter=10000))])\n",
    "cv_poly3_model.fit(df_train[p1_features], df_train['WON'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see what `C` our model picked using cross validation by looking at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00024771])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_poly3_model.named_steps[\"model\"].C_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05720566])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_poly3_model.named_steps[\"model\"].intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.71997659e-07,  1.08691295e-02, -1.08452761e-02, ...,\n",
       "         1.22570679e-02,  9.82332358e-04,  1.31474179e-02]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_poly3_model.named_steps[\"model\"].coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, compute the training and test set accuracy for `cv_poly3_model`. On my computer, I got 85% on the training set, and 81% on the test set.\n",
    "\n",
    "We can see that while our model does not perform as well on the training set, it generalizes much better to our unseen test set than our original model `unregularized_poly3_model`, which only was able to achieve 73% accuracy.\n",
    "\n",
    "**Bottom line:** `cv_poly3_model` does the best job, and it is able to do this by applying regularization, with hyperparameter C selected through cross validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8505"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_train[\"WON\"], cv_poly3_model.predict(df_train[p1_features]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.808695652173913"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_test[\"WON\"], cv_poly3_model.predict(df_test[p1_features]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bonus Problem 1F: L1 Regularization (OPTIONAL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like linear regression, we can also use L1 regularization. That is, instead of adding a penalty term that looks like $\\sum \\theta_i^2$, it looks like $\\sum |\\theta_i|$.\n",
    "\n",
    "In HW4, bonus problem 2H, we explored this. Create a model `p1e_model` below that is just like `cv_poly3_model`, except that it uses L1 regularization. The result is that most parameters will be zero.\n",
    "\n",
    "To use L1 regularization, set `penalty = l1` and set `solver = 'liblinear'`. \n",
    "\n",
    "This might several minutes to finish running, depending on your computer. Consider reducing the number of Cs if you don't want to wait that long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('poly',\n",
       "                 PolynomialFeatures(degree=3, include_bias=True,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LogisticRegressionCV(Cs=array([1.00000000e-07, 1.32194115e-07, 1.74752840e-07, 2.31012970e-07,\n",
       "       3.05385551e-07, 4.03701726e-07, 5.33669923e-07, 7.05480231e-07,\n",
       "       9.326033...\n",
       "       1.41747416e+04, 1.87381742e+04, 2.47707636e+04, 3.27454916e+04,\n",
       "       4.32876128e+04, 5.72236766e+04, 7.56463328e+04, 1.00000000e+05]),\n",
       "                                      class_weight=None, cv=3, dual=False,\n",
       "                                      fit_intercept=True, intercept_scaling=1.0,\n",
       "                                      l1_ratios=None, max_iter=10000,\n",
       "                                      multi_class='auto', n_jobs=-1,\n",
       "                                      penalty='l1', random_state=None,\n",
       "                                      refit=True, scoring=None,\n",
       "                                      solver='liblinear', tol=0.0001,\n",
       "                                      verbose=0))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1f_model = Pipeline([('scale', StandardScaler()),\n",
    "                      ('poly', PolynomialFeatures(3)),\n",
    "                      ('model',\n",
    "                       LogisticRegressionCV(penalty='l1',\n",
    "                                            solver='liblinear',\n",
    "                                            max_iter=10000,\n",
    "                                            cv=3,\n",
    "                                            Cs=10**np.linspace(-7, 5, 100),\n",
    "                                            n_jobs=-1))])\n",
    "p1f_model.fit(df_train[p1_features], df_train['WON'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04977024])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1f_model.named_steps[\"model\"].C_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1f_model.named_steps[\"model\"].intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.        , -0.25674936, ...,  0.        ,\n",
       "         0.        ,  0.        ]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1f_model.named_steps[\"model\"].coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, similar to problem 2H from exercise 4, create a table of all non-zero coefficients along with their names. You should have around 100 non-zero features, out of a total of 1,330."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1',\n",
       " 'FGM',\n",
       " 'FGA',\n",
       " 'FG_PCT',\n",
       " 'FG3M',\n",
       " 'FG3A',\n",
       " 'FG3_PCT',\n",
       " 'FTM',\n",
       " 'FTA',\n",
       " 'FT_PCT',\n",
       " 'OREB',\n",
       " 'DREB',\n",
       " 'REB',\n",
       " 'AST',\n",
       " 'STL',\n",
       " 'BLK',\n",
       " 'TOV',\n",
       " 'PF',\n",
       " 'PTS',\n",
       " 'FGM^2',\n",
       " 'FGM FGA',\n",
       " 'FGM FG_PCT',\n",
       " 'FGM FG3M',\n",
       " 'FGM FG3A',\n",
       " 'FGM FG3_PCT',\n",
       " 'FGM FTM',\n",
       " 'FGM FTA',\n",
       " 'FGM FT_PCT',\n",
       " 'FGM OREB',\n",
       " 'FGM DREB',\n",
       " 'FGM REB',\n",
       " 'FGM AST',\n",
       " 'FGM STL',\n",
       " 'FGM BLK',\n",
       " 'FGM TOV',\n",
       " 'FGM PF',\n",
       " 'FGM PTS',\n",
       " 'FGA^2',\n",
       " 'FGA FG_PCT',\n",
       " 'FGA FG3M',\n",
       " 'FGA FG3A',\n",
       " 'FGA FG3_PCT',\n",
       " 'FGA FTM',\n",
       " 'FGA FTA',\n",
       " 'FGA FT_PCT',\n",
       " 'FGA OREB',\n",
       " 'FGA DREB',\n",
       " 'FGA REB',\n",
       " 'FGA AST',\n",
       " 'FGA STL',\n",
       " 'FGA BLK',\n",
       " 'FGA TOV',\n",
       " 'FGA PF',\n",
       " 'FGA PTS',\n",
       " 'FG_PCT^2',\n",
       " 'FG_PCT FG3M',\n",
       " 'FG_PCT FG3A',\n",
       " 'FG_PCT FG3_PCT',\n",
       " 'FG_PCT FTM',\n",
       " 'FG_PCT FTA',\n",
       " 'FG_PCT FT_PCT',\n",
       " 'FG_PCT OREB',\n",
       " 'FG_PCT DREB',\n",
       " 'FG_PCT REB',\n",
       " 'FG_PCT AST',\n",
       " 'FG_PCT STL',\n",
       " 'FG_PCT BLK',\n",
       " 'FG_PCT TOV',\n",
       " 'FG_PCT PF',\n",
       " 'FG_PCT PTS',\n",
       " 'FG3M^2',\n",
       " 'FG3M FG3A',\n",
       " 'FG3M FG3_PCT',\n",
       " 'FG3M FTM',\n",
       " 'FG3M FTA',\n",
       " 'FG3M FT_PCT',\n",
       " 'FG3M OREB',\n",
       " 'FG3M DREB',\n",
       " 'FG3M REB',\n",
       " 'FG3M AST',\n",
       " 'FG3M STL',\n",
       " 'FG3M BLK',\n",
       " 'FG3M TOV',\n",
       " 'FG3M PF',\n",
       " 'FG3M PTS',\n",
       " 'FG3A^2',\n",
       " 'FG3A FG3_PCT',\n",
       " 'FG3A FTM',\n",
       " 'FG3A FTA',\n",
       " 'FG3A FT_PCT',\n",
       " 'FG3A OREB',\n",
       " 'FG3A DREB',\n",
       " 'FG3A REB',\n",
       " 'FG3A AST',\n",
       " 'FG3A STL',\n",
       " 'FG3A BLK',\n",
       " 'FG3A TOV',\n",
       " 'FG3A PF',\n",
       " 'FG3A PTS',\n",
       " 'FG3_PCT^2',\n",
       " 'FG3_PCT FTM',\n",
       " 'FG3_PCT FTA',\n",
       " 'FG3_PCT FT_PCT',\n",
       " 'FG3_PCT OREB',\n",
       " 'FG3_PCT DREB',\n",
       " 'FG3_PCT REB',\n",
       " 'FG3_PCT AST',\n",
       " 'FG3_PCT STL',\n",
       " 'FG3_PCT BLK',\n",
       " 'FG3_PCT TOV',\n",
       " 'FG3_PCT PF',\n",
       " 'FG3_PCT PTS',\n",
       " 'FTM^2',\n",
       " 'FTM FTA',\n",
       " 'FTM FT_PCT',\n",
       " 'FTM OREB',\n",
       " 'FTM DREB',\n",
       " 'FTM REB',\n",
       " 'FTM AST',\n",
       " 'FTM STL',\n",
       " 'FTM BLK',\n",
       " 'FTM TOV',\n",
       " 'FTM PF',\n",
       " 'FTM PTS',\n",
       " 'FTA^2',\n",
       " 'FTA FT_PCT',\n",
       " 'FTA OREB',\n",
       " 'FTA DREB',\n",
       " 'FTA REB',\n",
       " 'FTA AST',\n",
       " 'FTA STL',\n",
       " 'FTA BLK',\n",
       " 'FTA TOV',\n",
       " 'FTA PF',\n",
       " 'FTA PTS',\n",
       " 'FT_PCT^2',\n",
       " 'FT_PCT OREB',\n",
       " 'FT_PCT DREB',\n",
       " 'FT_PCT REB',\n",
       " 'FT_PCT AST',\n",
       " 'FT_PCT STL',\n",
       " 'FT_PCT BLK',\n",
       " 'FT_PCT TOV',\n",
       " 'FT_PCT PF',\n",
       " 'FT_PCT PTS',\n",
       " 'OREB^2',\n",
       " 'OREB DREB',\n",
       " 'OREB REB',\n",
       " 'OREB AST',\n",
       " 'OREB STL',\n",
       " 'OREB BLK',\n",
       " 'OREB TOV',\n",
       " 'OREB PF',\n",
       " 'OREB PTS',\n",
       " 'DREB^2',\n",
       " 'DREB REB',\n",
       " 'DREB AST',\n",
       " 'DREB STL',\n",
       " 'DREB BLK',\n",
       " 'DREB TOV',\n",
       " 'DREB PF',\n",
       " 'DREB PTS',\n",
       " 'REB^2',\n",
       " 'REB AST',\n",
       " 'REB STL',\n",
       " 'REB BLK',\n",
       " 'REB TOV',\n",
       " 'REB PF',\n",
       " 'REB PTS',\n",
       " 'AST^2',\n",
       " 'AST STL',\n",
       " 'AST BLK',\n",
       " 'AST TOV',\n",
       " 'AST PF',\n",
       " 'AST PTS',\n",
       " 'STL^2',\n",
       " 'STL BLK',\n",
       " 'STL TOV',\n",
       " 'STL PF',\n",
       " 'STL PTS',\n",
       " 'BLK^2',\n",
       " 'BLK TOV',\n",
       " 'BLK PF',\n",
       " 'BLK PTS',\n",
       " 'TOV^2',\n",
       " 'TOV PF',\n",
       " 'TOV PTS',\n",
       " 'PF^2',\n",
       " 'PF PTS',\n",
       " 'PTS^2',\n",
       " 'FGM^3',\n",
       " 'FGM^2 FGA',\n",
       " 'FGM^2 FG_PCT',\n",
       " 'FGM^2 FG3M',\n",
       " 'FGM^2 FG3A',\n",
       " 'FGM^2 FG3_PCT',\n",
       " 'FGM^2 FTM',\n",
       " 'FGM^2 FTA',\n",
       " 'FGM^2 FT_PCT',\n",
       " 'FGM^2 OREB',\n",
       " 'FGM^2 DREB',\n",
       " 'FGM^2 REB',\n",
       " 'FGM^2 AST',\n",
       " 'FGM^2 STL',\n",
       " 'FGM^2 BLK',\n",
       " 'FGM^2 TOV',\n",
       " 'FGM^2 PF',\n",
       " 'FGM^2 PTS',\n",
       " 'FGM FGA^2',\n",
       " 'FGM FGA FG_PCT',\n",
       " 'FGM FGA FG3M',\n",
       " 'FGM FGA FG3A',\n",
       " 'FGM FGA FG3_PCT',\n",
       " 'FGM FGA FTM',\n",
       " 'FGM FGA FTA',\n",
       " 'FGM FGA FT_PCT',\n",
       " 'FGM FGA OREB',\n",
       " 'FGM FGA DREB',\n",
       " 'FGM FGA REB',\n",
       " 'FGM FGA AST',\n",
       " 'FGM FGA STL',\n",
       " 'FGM FGA BLK',\n",
       " 'FGM FGA TOV',\n",
       " 'FGM FGA PF',\n",
       " 'FGM FGA PTS',\n",
       " 'FGM FG_PCT^2',\n",
       " 'FGM FG_PCT FG3M',\n",
       " 'FGM FG_PCT FG3A',\n",
       " 'FGM FG_PCT FG3_PCT',\n",
       " 'FGM FG_PCT FTM',\n",
       " 'FGM FG_PCT FTA',\n",
       " 'FGM FG_PCT FT_PCT',\n",
       " 'FGM FG_PCT OREB',\n",
       " 'FGM FG_PCT DREB',\n",
       " 'FGM FG_PCT REB',\n",
       " 'FGM FG_PCT AST',\n",
       " 'FGM FG_PCT STL',\n",
       " 'FGM FG_PCT BLK',\n",
       " 'FGM FG_PCT TOV',\n",
       " 'FGM FG_PCT PF',\n",
       " 'FGM FG_PCT PTS',\n",
       " 'FGM FG3M^2',\n",
       " 'FGM FG3M FG3A',\n",
       " 'FGM FG3M FG3_PCT',\n",
       " 'FGM FG3M FTM',\n",
       " 'FGM FG3M FTA',\n",
       " 'FGM FG3M FT_PCT',\n",
       " 'FGM FG3M OREB',\n",
       " 'FGM FG3M DREB',\n",
       " 'FGM FG3M REB',\n",
       " 'FGM FG3M AST',\n",
       " 'FGM FG3M STL',\n",
       " 'FGM FG3M BLK',\n",
       " 'FGM FG3M TOV',\n",
       " 'FGM FG3M PF',\n",
       " 'FGM FG3M PTS',\n",
       " 'FGM FG3A^2',\n",
       " 'FGM FG3A FG3_PCT',\n",
       " 'FGM FG3A FTM',\n",
       " 'FGM FG3A FTA',\n",
       " 'FGM FG3A FT_PCT',\n",
       " 'FGM FG3A OREB',\n",
       " 'FGM FG3A DREB',\n",
       " 'FGM FG3A REB',\n",
       " 'FGM FG3A AST',\n",
       " 'FGM FG3A STL',\n",
       " 'FGM FG3A BLK',\n",
       " 'FGM FG3A TOV',\n",
       " 'FGM FG3A PF',\n",
       " 'FGM FG3A PTS',\n",
       " 'FGM FG3_PCT^2',\n",
       " 'FGM FG3_PCT FTM',\n",
       " 'FGM FG3_PCT FTA',\n",
       " 'FGM FG3_PCT FT_PCT',\n",
       " 'FGM FG3_PCT OREB',\n",
       " 'FGM FG3_PCT DREB',\n",
       " 'FGM FG3_PCT REB',\n",
       " 'FGM FG3_PCT AST',\n",
       " 'FGM FG3_PCT STL',\n",
       " 'FGM FG3_PCT BLK',\n",
       " 'FGM FG3_PCT TOV',\n",
       " 'FGM FG3_PCT PF',\n",
       " 'FGM FG3_PCT PTS',\n",
       " 'FGM FTM^2',\n",
       " 'FGM FTM FTA',\n",
       " 'FGM FTM FT_PCT',\n",
       " 'FGM FTM OREB',\n",
       " 'FGM FTM DREB',\n",
       " 'FGM FTM REB',\n",
       " 'FGM FTM AST',\n",
       " 'FGM FTM STL',\n",
       " 'FGM FTM BLK',\n",
       " 'FGM FTM TOV',\n",
       " 'FGM FTM PF',\n",
       " 'FGM FTM PTS',\n",
       " 'FGM FTA^2',\n",
       " 'FGM FTA FT_PCT',\n",
       " 'FGM FTA OREB',\n",
       " 'FGM FTA DREB',\n",
       " 'FGM FTA REB',\n",
       " 'FGM FTA AST',\n",
       " 'FGM FTA STL',\n",
       " 'FGM FTA BLK',\n",
       " 'FGM FTA TOV',\n",
       " 'FGM FTA PF',\n",
       " 'FGM FTA PTS',\n",
       " 'FGM FT_PCT^2',\n",
       " 'FGM FT_PCT OREB',\n",
       " 'FGM FT_PCT DREB',\n",
       " 'FGM FT_PCT REB',\n",
       " 'FGM FT_PCT AST',\n",
       " 'FGM FT_PCT STL',\n",
       " 'FGM FT_PCT BLK',\n",
       " 'FGM FT_PCT TOV',\n",
       " 'FGM FT_PCT PF',\n",
       " 'FGM FT_PCT PTS',\n",
       " 'FGM OREB^2',\n",
       " 'FGM OREB DREB',\n",
       " 'FGM OREB REB',\n",
       " 'FGM OREB AST',\n",
       " 'FGM OREB STL',\n",
       " 'FGM OREB BLK',\n",
       " 'FGM OREB TOV',\n",
       " 'FGM OREB PF',\n",
       " 'FGM OREB PTS',\n",
       " 'FGM DREB^2',\n",
       " 'FGM DREB REB',\n",
       " 'FGM DREB AST',\n",
       " 'FGM DREB STL',\n",
       " 'FGM DREB BLK',\n",
       " 'FGM DREB TOV',\n",
       " 'FGM DREB PF',\n",
       " 'FGM DREB PTS',\n",
       " 'FGM REB^2',\n",
       " 'FGM REB AST',\n",
       " 'FGM REB STL',\n",
       " 'FGM REB BLK',\n",
       " 'FGM REB TOV',\n",
       " 'FGM REB PF',\n",
       " 'FGM REB PTS',\n",
       " 'FGM AST^2',\n",
       " 'FGM AST STL',\n",
       " 'FGM AST BLK',\n",
       " 'FGM AST TOV',\n",
       " 'FGM AST PF',\n",
       " 'FGM AST PTS',\n",
       " 'FGM STL^2',\n",
       " 'FGM STL BLK',\n",
       " 'FGM STL TOV',\n",
       " 'FGM STL PF',\n",
       " 'FGM STL PTS',\n",
       " 'FGM BLK^2',\n",
       " 'FGM BLK TOV',\n",
       " 'FGM BLK PF',\n",
       " 'FGM BLK PTS',\n",
       " 'FGM TOV^2',\n",
       " 'FGM TOV PF',\n",
       " 'FGM TOV PTS',\n",
       " 'FGM PF^2',\n",
       " 'FGM PF PTS',\n",
       " 'FGM PTS^2',\n",
       " 'FGA^3',\n",
       " 'FGA^2 FG_PCT',\n",
       " 'FGA^2 FG3M',\n",
       " 'FGA^2 FG3A',\n",
       " 'FGA^2 FG3_PCT',\n",
       " 'FGA^2 FTM',\n",
       " 'FGA^2 FTA',\n",
       " 'FGA^2 FT_PCT',\n",
       " 'FGA^2 OREB',\n",
       " 'FGA^2 DREB',\n",
       " 'FGA^2 REB',\n",
       " 'FGA^2 AST',\n",
       " 'FGA^2 STL',\n",
       " 'FGA^2 BLK',\n",
       " 'FGA^2 TOV',\n",
       " 'FGA^2 PF',\n",
       " 'FGA^2 PTS',\n",
       " 'FGA FG_PCT^2',\n",
       " 'FGA FG_PCT FG3M',\n",
       " 'FGA FG_PCT FG3A',\n",
       " 'FGA FG_PCT FG3_PCT',\n",
       " 'FGA FG_PCT FTM',\n",
       " 'FGA FG_PCT FTA',\n",
       " 'FGA FG_PCT FT_PCT',\n",
       " 'FGA FG_PCT OREB',\n",
       " 'FGA FG_PCT DREB',\n",
       " 'FGA FG_PCT REB',\n",
       " 'FGA FG_PCT AST',\n",
       " 'FGA FG_PCT STL',\n",
       " 'FGA FG_PCT BLK',\n",
       " 'FGA FG_PCT TOV',\n",
       " 'FGA FG_PCT PF',\n",
       " 'FGA FG_PCT PTS',\n",
       " 'FGA FG3M^2',\n",
       " 'FGA FG3M FG3A',\n",
       " 'FGA FG3M FG3_PCT',\n",
       " 'FGA FG3M FTM',\n",
       " 'FGA FG3M FTA',\n",
       " 'FGA FG3M FT_PCT',\n",
       " 'FGA FG3M OREB',\n",
       " 'FGA FG3M DREB',\n",
       " 'FGA FG3M REB',\n",
       " 'FGA FG3M AST',\n",
       " 'FGA FG3M STL',\n",
       " 'FGA FG3M BLK',\n",
       " 'FGA FG3M TOV',\n",
       " 'FGA FG3M PF',\n",
       " 'FGA FG3M PTS',\n",
       " 'FGA FG3A^2',\n",
       " 'FGA FG3A FG3_PCT',\n",
       " 'FGA FG3A FTM',\n",
       " 'FGA FG3A FTA',\n",
       " 'FGA FG3A FT_PCT',\n",
       " 'FGA FG3A OREB',\n",
       " 'FGA FG3A DREB',\n",
       " 'FGA FG3A REB',\n",
       " 'FGA FG3A AST',\n",
       " 'FGA FG3A STL',\n",
       " 'FGA FG3A BLK',\n",
       " 'FGA FG3A TOV',\n",
       " 'FGA FG3A PF',\n",
       " 'FGA FG3A PTS',\n",
       " 'FGA FG3_PCT^2',\n",
       " 'FGA FG3_PCT FTM',\n",
       " 'FGA FG3_PCT FTA',\n",
       " 'FGA FG3_PCT FT_PCT',\n",
       " 'FGA FG3_PCT OREB',\n",
       " 'FGA FG3_PCT DREB',\n",
       " 'FGA FG3_PCT REB',\n",
       " 'FGA FG3_PCT AST',\n",
       " 'FGA FG3_PCT STL',\n",
       " 'FGA FG3_PCT BLK',\n",
       " 'FGA FG3_PCT TOV',\n",
       " 'FGA FG3_PCT PF',\n",
       " 'FGA FG3_PCT PTS',\n",
       " 'FGA FTM^2',\n",
       " 'FGA FTM FTA',\n",
       " 'FGA FTM FT_PCT',\n",
       " 'FGA FTM OREB',\n",
       " 'FGA FTM DREB',\n",
       " 'FGA FTM REB',\n",
       " 'FGA FTM AST',\n",
       " 'FGA FTM STL',\n",
       " 'FGA FTM BLK',\n",
       " 'FGA FTM TOV',\n",
       " 'FGA FTM PF',\n",
       " 'FGA FTM PTS',\n",
       " 'FGA FTA^2',\n",
       " 'FGA FTA FT_PCT',\n",
       " 'FGA FTA OREB',\n",
       " 'FGA FTA DREB',\n",
       " 'FGA FTA REB',\n",
       " 'FGA FTA AST',\n",
       " 'FGA FTA STL',\n",
       " 'FGA FTA BLK',\n",
       " 'FGA FTA TOV',\n",
       " 'FGA FTA PF',\n",
       " 'FGA FTA PTS',\n",
       " 'FGA FT_PCT^2',\n",
       " 'FGA FT_PCT OREB',\n",
       " 'FGA FT_PCT DREB',\n",
       " 'FGA FT_PCT REB',\n",
       " 'FGA FT_PCT AST',\n",
       " 'FGA FT_PCT STL',\n",
       " 'FGA FT_PCT BLK',\n",
       " 'FGA FT_PCT TOV',\n",
       " 'FGA FT_PCT PF',\n",
       " 'FGA FT_PCT PTS',\n",
       " 'FGA OREB^2',\n",
       " 'FGA OREB DREB',\n",
       " 'FGA OREB REB',\n",
       " 'FGA OREB AST',\n",
       " 'FGA OREB STL',\n",
       " 'FGA OREB BLK',\n",
       " 'FGA OREB TOV',\n",
       " 'FGA OREB PF',\n",
       " 'FGA OREB PTS',\n",
       " 'FGA DREB^2',\n",
       " 'FGA DREB REB',\n",
       " 'FGA DREB AST',\n",
       " 'FGA DREB STL',\n",
       " 'FGA DREB BLK',\n",
       " 'FGA DREB TOV',\n",
       " 'FGA DREB PF',\n",
       " 'FGA DREB PTS',\n",
       " 'FGA REB^2',\n",
       " 'FGA REB AST',\n",
       " 'FGA REB STL',\n",
       " 'FGA REB BLK',\n",
       " 'FGA REB TOV',\n",
       " 'FGA REB PF',\n",
       " 'FGA REB PTS',\n",
       " 'FGA AST^2',\n",
       " 'FGA AST STL',\n",
       " 'FGA AST BLK',\n",
       " 'FGA AST TOV',\n",
       " 'FGA AST PF',\n",
       " 'FGA AST PTS',\n",
       " 'FGA STL^2',\n",
       " 'FGA STL BLK',\n",
       " 'FGA STL TOV',\n",
       " 'FGA STL PF',\n",
       " 'FGA STL PTS',\n",
       " 'FGA BLK^2',\n",
       " 'FGA BLK TOV',\n",
       " 'FGA BLK PF',\n",
       " 'FGA BLK PTS',\n",
       " 'FGA TOV^2',\n",
       " 'FGA TOV PF',\n",
       " 'FGA TOV PTS',\n",
       " 'FGA PF^2',\n",
       " 'FGA PF PTS',\n",
       " 'FGA PTS^2',\n",
       " 'FG_PCT^3',\n",
       " 'FG_PCT^2 FG3M',\n",
       " 'FG_PCT^2 FG3A',\n",
       " 'FG_PCT^2 FG3_PCT',\n",
       " 'FG_PCT^2 FTM',\n",
       " 'FG_PCT^2 FTA',\n",
       " 'FG_PCT^2 FT_PCT',\n",
       " 'FG_PCT^2 OREB',\n",
       " 'FG_PCT^2 DREB',\n",
       " 'FG_PCT^2 REB',\n",
       " 'FG_PCT^2 AST',\n",
       " 'FG_PCT^2 STL',\n",
       " 'FG_PCT^2 BLK',\n",
       " 'FG_PCT^2 TOV',\n",
       " 'FG_PCT^2 PF',\n",
       " 'FG_PCT^2 PTS',\n",
       " 'FG_PCT FG3M^2',\n",
       " 'FG_PCT FG3M FG3A',\n",
       " 'FG_PCT FG3M FG3_PCT',\n",
       " 'FG_PCT FG3M FTM',\n",
       " 'FG_PCT FG3M FTA',\n",
       " 'FG_PCT FG3M FT_PCT',\n",
       " 'FG_PCT FG3M OREB',\n",
       " 'FG_PCT FG3M DREB',\n",
       " 'FG_PCT FG3M REB',\n",
       " 'FG_PCT FG3M AST',\n",
       " 'FG_PCT FG3M STL',\n",
       " 'FG_PCT FG3M BLK',\n",
       " 'FG_PCT FG3M TOV',\n",
       " 'FG_PCT FG3M PF',\n",
       " 'FG_PCT FG3M PTS',\n",
       " 'FG_PCT FG3A^2',\n",
       " 'FG_PCT FG3A FG3_PCT',\n",
       " 'FG_PCT FG3A FTM',\n",
       " 'FG_PCT FG3A FTA',\n",
       " 'FG_PCT FG3A FT_PCT',\n",
       " 'FG_PCT FG3A OREB',\n",
       " 'FG_PCT FG3A DREB',\n",
       " 'FG_PCT FG3A REB',\n",
       " 'FG_PCT FG3A AST',\n",
       " 'FG_PCT FG3A STL',\n",
       " 'FG_PCT FG3A BLK',\n",
       " 'FG_PCT FG3A TOV',\n",
       " 'FG_PCT FG3A PF',\n",
       " 'FG_PCT FG3A PTS',\n",
       " 'FG_PCT FG3_PCT^2',\n",
       " 'FG_PCT FG3_PCT FTM',\n",
       " 'FG_PCT FG3_PCT FTA',\n",
       " 'FG_PCT FG3_PCT FT_PCT',\n",
       " 'FG_PCT FG3_PCT OREB',\n",
       " 'FG_PCT FG3_PCT DREB',\n",
       " 'FG_PCT FG3_PCT REB',\n",
       " 'FG_PCT FG3_PCT AST',\n",
       " 'FG_PCT FG3_PCT STL',\n",
       " 'FG_PCT FG3_PCT BLK',\n",
       " 'FG_PCT FG3_PCT TOV',\n",
       " 'FG_PCT FG3_PCT PF',\n",
       " 'FG_PCT FG3_PCT PTS',\n",
       " 'FG_PCT FTM^2',\n",
       " 'FG_PCT FTM FTA',\n",
       " 'FG_PCT FTM FT_PCT',\n",
       " 'FG_PCT FTM OREB',\n",
       " 'FG_PCT FTM DREB',\n",
       " 'FG_PCT FTM REB',\n",
       " 'FG_PCT FTM AST',\n",
       " 'FG_PCT FTM STL',\n",
       " 'FG_PCT FTM BLK',\n",
       " 'FG_PCT FTM TOV',\n",
       " 'FG_PCT FTM PF',\n",
       " 'FG_PCT FTM PTS',\n",
       " 'FG_PCT FTA^2',\n",
       " 'FG_PCT FTA FT_PCT',\n",
       " 'FG_PCT FTA OREB',\n",
       " 'FG_PCT FTA DREB',\n",
       " 'FG_PCT FTA REB',\n",
       " 'FG_PCT FTA AST',\n",
       " 'FG_PCT FTA STL',\n",
       " 'FG_PCT FTA BLK',\n",
       " 'FG_PCT FTA TOV',\n",
       " 'FG_PCT FTA PF',\n",
       " 'FG_PCT FTA PTS',\n",
       " 'FG_PCT FT_PCT^2',\n",
       " 'FG_PCT FT_PCT OREB',\n",
       " 'FG_PCT FT_PCT DREB',\n",
       " 'FG_PCT FT_PCT REB',\n",
       " 'FG_PCT FT_PCT AST',\n",
       " 'FG_PCT FT_PCT STL',\n",
       " 'FG_PCT FT_PCT BLK',\n",
       " 'FG_PCT FT_PCT TOV',\n",
       " 'FG_PCT FT_PCT PF',\n",
       " 'FG_PCT FT_PCT PTS',\n",
       " 'FG_PCT OREB^2',\n",
       " 'FG_PCT OREB DREB',\n",
       " 'FG_PCT OREB REB',\n",
       " 'FG_PCT OREB AST',\n",
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       " 'FG_PCT REB PF',\n",
       " 'FG_PCT REB PTS',\n",
       " 'FG_PCT AST^2',\n",
       " 'FG_PCT AST STL',\n",
       " 'FG_PCT AST BLK',\n",
       " 'FG_PCT AST TOV',\n",
       " 'FG_PCT AST PF',\n",
       " 'FG_PCT AST PTS',\n",
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       " 'FG_PCT STL BLK',\n",
       " 'FG_PCT STL TOV',\n",
       " 'FG_PCT STL PF',\n",
       " 'FG_PCT STL PTS',\n",
       " 'FG_PCT BLK^2',\n",
       " 'FG_PCT BLK TOV',\n",
       " 'FG_PCT BLK PF',\n",
       " 'FG_PCT BLK PTS',\n",
       " 'FG_PCT TOV^2',\n",
       " 'FG_PCT TOV PF',\n",
       " 'FG_PCT TOV PTS',\n",
       " 'FG_PCT PF^2',\n",
       " 'FG_PCT PF PTS',\n",
       " 'FG_PCT PTS^2',\n",
       " 'FG3M^3',\n",
       " 'FG3M^2 FG3A',\n",
       " 'FG3M^2 FG3_PCT',\n",
       " 'FG3M^2 FTM',\n",
       " 'FG3M^2 FTA',\n",
       " 'FG3M^2 FT_PCT',\n",
       " 'FG3M^2 OREB',\n",
       " 'FG3M^2 DREB',\n",
       " 'FG3M^2 REB',\n",
       " 'FG3M^2 AST',\n",
       " 'FG3M^2 STL',\n",
       " 'FG3M^2 BLK',\n",
       " 'FG3M^2 TOV',\n",
       " 'FG3M^2 PF',\n",
       " 'FG3M^2 PTS',\n",
       " 'FG3M FG3A^2',\n",
       " 'FG3M FG3A FG3_PCT',\n",
       " 'FG3M FG3A FTM',\n",
       " 'FG3M FG3A FTA',\n",
       " 'FG3M FG3A FT_PCT',\n",
       " 'FG3M FG3A OREB',\n",
       " 'FG3M FG3A DREB',\n",
       " 'FG3M FG3A REB',\n",
       " 'FG3M FG3A AST',\n",
       " 'FG3M FG3A STL',\n",
       " 'FG3M FG3A BLK',\n",
       " 'FG3M FG3A TOV',\n",
       " 'FG3M FG3A PF',\n",
       " 'FG3M FG3A PTS',\n",
       " 'FG3M FG3_PCT^2',\n",
       " 'FG3M FG3_PCT FTM',\n",
       " 'FG3M FG3_PCT FTA',\n",
       " 'FG3M FG3_PCT FT_PCT',\n",
       " 'FG3M FG3_PCT OREB',\n",
       " 'FG3M FG3_PCT DREB',\n",
       " 'FG3M FG3_PCT REB',\n",
       " 'FG3M FG3_PCT AST',\n",
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       " 'FG3M FG3_PCT BLK',\n",
       " 'FG3M FG3_PCT TOV',\n",
       " 'FG3M FG3_PCT PF',\n",
       " 'FG3M FG3_PCT PTS',\n",
       " 'FG3M FTM^2',\n",
       " 'FG3M FTM FTA',\n",
       " 'FG3M FTM FT_PCT',\n",
       " 'FG3M FTM OREB',\n",
       " 'FG3M FTM DREB',\n",
       " 'FG3M FTM REB',\n",
       " 'FG3M FTM AST',\n",
       " 'FG3M FTM STL',\n",
       " 'FG3M FTM BLK',\n",
       " 'FG3M FTM TOV',\n",
       " 'FG3M FTM PF',\n",
       " 'FG3M FTM PTS',\n",
       " 'FG3M FTA^2',\n",
       " 'FG3M FTA FT_PCT',\n",
       " 'FG3M FTA OREB',\n",
       " 'FG3M FTA DREB',\n",
       " 'FG3M FTA REB',\n",
       " 'FG3M FTA AST',\n",
       " 'FG3M FTA STL',\n",
       " 'FG3M FTA BLK',\n",
       " 'FG3M FTA TOV',\n",
       " 'FG3M FTA PF',\n",
       " 'FG3M FTA PTS',\n",
       " 'FG3M FT_PCT^2',\n",
       " 'FG3M FT_PCT OREB',\n",
       " 'FG3M FT_PCT DREB',\n",
       " 'FG3M FT_PCT REB',\n",
       " 'FG3M FT_PCT AST',\n",
       " 'FG3M FT_PCT STL',\n",
       " 'FG3M FT_PCT BLK',\n",
       " 'FG3M FT_PCT TOV',\n",
       " 'FG3M FT_PCT PF',\n",
       " 'FG3M FT_PCT PTS',\n",
       " 'FG3M OREB^2',\n",
       " 'FG3M OREB DREB',\n",
       " 'FG3M OREB REB',\n",
       " 'FG3M OREB AST',\n",
       " 'FG3M OREB STL',\n",
       " 'FG3M OREB BLK',\n",
       " 'FG3M OREB TOV',\n",
       " 'FG3M OREB PF',\n",
       " 'FG3M OREB PTS',\n",
       " 'FG3M DREB^2',\n",
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       " 'FG3M DREB AST',\n",
       " 'FG3M DREB STL',\n",
       " 'FG3M DREB BLK',\n",
       " 'FG3M DREB TOV',\n",
       " 'FG3M DREB PF',\n",
       " 'FG3M DREB PTS',\n",
       " 'FG3M REB^2',\n",
       " 'FG3M REB AST',\n",
       " 'FG3M REB STL',\n",
       " 'FG3M REB BLK',\n",
       " 'FG3M REB TOV',\n",
       " 'FG3M REB PF',\n",
       " 'FG3M REB PTS',\n",
       " 'FG3M AST^2',\n",
       " 'FG3M AST STL',\n",
       " 'FG3M AST BLK',\n",
       " 'FG3M AST TOV',\n",
       " 'FG3M AST PF',\n",
       " 'FG3M AST PTS',\n",
       " 'FG3M STL^2',\n",
       " 'FG3M STL BLK',\n",
       " 'FG3M STL TOV',\n",
       " 'FG3M STL PF',\n",
       " 'FG3M STL PTS',\n",
       " 'FG3M BLK^2',\n",
       " 'FG3M BLK TOV',\n",
       " 'FG3M BLK PF',\n",
       " 'FG3M BLK PTS',\n",
       " 'FG3M TOV^2',\n",
       " 'FG3M TOV PF',\n",
       " 'FG3M TOV PTS',\n",
       " 'FG3M PF^2',\n",
       " 'FG3M PF PTS',\n",
       " 'FG3M PTS^2',\n",
       " 'FG3A^3',\n",
       " 'FG3A^2 FG3_PCT',\n",
       " 'FG3A^2 FTM',\n",
       " 'FG3A^2 FTA',\n",
       " 'FG3A^2 FT_PCT',\n",
       " 'FG3A^2 OREB',\n",
       " 'FG3A^2 DREB',\n",
       " 'FG3A^2 REB',\n",
       " 'FG3A^2 AST',\n",
       " 'FG3A^2 STL',\n",
       " 'FG3A^2 BLK',\n",
       " 'FG3A^2 TOV',\n",
       " 'FG3A^2 PF',\n",
       " 'FG3A^2 PTS',\n",
       " 'FG3A FG3_PCT^2',\n",
       " 'FG3A FG3_PCT FTM',\n",
       " 'FG3A FG3_PCT FTA',\n",
       " 'FG3A FG3_PCT FT_PCT',\n",
       " 'FG3A FG3_PCT OREB',\n",
       " 'FG3A FG3_PCT DREB',\n",
       " 'FG3A FG3_PCT REB',\n",
       " 'FG3A FG3_PCT AST',\n",
       " 'FG3A FG3_PCT STL',\n",
       " 'FG3A FG3_PCT BLK',\n",
       " 'FG3A FG3_PCT TOV',\n",
       " 'FG3A FG3_PCT PF',\n",
       " 'FG3A FG3_PCT PTS',\n",
       " 'FG3A FTM^2',\n",
       " 'FG3A FTM FTA',\n",
       " 'FG3A FTM FT_PCT',\n",
       " 'FG3A FTM OREB',\n",
       " 'FG3A FTM DREB',\n",
       " 'FG3A FTM REB',\n",
       " 'FG3A FTM AST',\n",
       " 'FG3A FTM STL',\n",
       " 'FG3A FTM BLK',\n",
       " 'FG3A FTM TOV',\n",
       " 'FG3A FTM PF',\n",
       " 'FG3A FTM PTS',\n",
       " 'FG3A FTA^2',\n",
       " 'FG3A FTA FT_PCT',\n",
       " 'FG3A FTA OREB',\n",
       " 'FG3A FTA DREB',\n",
       " 'FG3A FTA REB',\n",
       " 'FG3A FTA AST',\n",
       " 'FG3A FTA STL',\n",
       " 'FG3A FTA BLK',\n",
       " 'FG3A FTA TOV',\n",
       " 'FG3A FTA PF',\n",
       " 'FG3A FTA PTS',\n",
       " 'FG3A FT_PCT^2',\n",
       " 'FG3A FT_PCT OREB',\n",
       " 'FG3A FT_PCT DREB',\n",
       " 'FG3A FT_PCT REB',\n",
       " 'FG3A FT_PCT AST',\n",
       " 'FG3A FT_PCT STL',\n",
       " 'FG3A FT_PCT BLK',\n",
       " 'FG3A FT_PCT TOV',\n",
       " 'FG3A FT_PCT PF',\n",
       " 'FG3A FT_PCT PTS',\n",
       " 'FG3A OREB^2',\n",
       " 'FG3A OREB DREB',\n",
       " 'FG3A OREB REB',\n",
       " 'FG3A OREB AST',\n",
       " 'FG3A OREB STL',\n",
       " 'FG3A OREB BLK',\n",
       " 'FG3A OREB TOV',\n",
       " 'FG3A OREB PF',\n",
       " 'FG3A OREB PTS',\n",
       " 'FG3A DREB^2',\n",
       " 'FG3A DREB REB',\n",
       " 'FG3A DREB AST',\n",
       " 'FG3A DREB STL',\n",
       " 'FG3A DREB BLK',\n",
       " 'FG3A DREB TOV',\n",
       " 'FG3A DREB PF',\n",
       " 'FG3A DREB PTS',\n",
       " 'FG3A REB^2',\n",
       " 'FG3A REB AST',\n",
       " 'FG3A REB STL',\n",
       " 'FG3A REB BLK',\n",
       " 'FG3A REB TOV',\n",
       " 'FG3A REB PF',\n",
       " 'FG3A REB PTS',\n",
       " 'FG3A AST^2',\n",
       " 'FG3A AST STL',\n",
       " 'FG3A AST BLK',\n",
       " 'FG3A AST TOV',\n",
       " 'FG3A AST PF',\n",
       " 'FG3A AST PTS',\n",
       " 'FG3A STL^2',\n",
       " 'FG3A STL BLK',\n",
       " 'FG3A STL TOV',\n",
       " 'FG3A STL PF',\n",
       " 'FG3A STL PTS',\n",
       " 'FG3A BLK^2',\n",
       " 'FG3A BLK TOV',\n",
       " 'FG3A BLK PF',\n",
       " 'FG3A BLK PTS',\n",
       " 'FG3A TOV^2',\n",
       " 'FG3A TOV PF',\n",
       " 'FG3A TOV PTS',\n",
       " 'FG3A PF^2',\n",
       " 'FG3A PF PTS',\n",
       " 'FG3A PTS^2',\n",
       " 'FG3_PCT^3',\n",
       " 'FG3_PCT^2 FTM',\n",
       " 'FG3_PCT^2 FTA',\n",
       " 'FG3_PCT^2 FT_PCT',\n",
       " 'FG3_PCT^2 OREB',\n",
       " 'FG3_PCT^2 DREB',\n",
       " 'FG3_PCT^2 REB',\n",
       " 'FG3_PCT^2 AST',\n",
       " 'FG3_PCT^2 STL',\n",
       " 'FG3_PCT^2 BLK',\n",
       " 'FG3_PCT^2 TOV',\n",
       " 'FG3_PCT^2 PF',\n",
       " 'FG3_PCT^2 PTS',\n",
       " 'FG3_PCT FTM^2',\n",
       " 'FG3_PCT FTM FTA',\n",
       " 'FG3_PCT FTM FT_PCT',\n",
       " 'FG3_PCT FTM OREB',\n",
       " 'FG3_PCT FTM DREB',\n",
       " 'FG3_PCT FTM REB',\n",
       " 'FG3_PCT FTM AST',\n",
       " 'FG3_PCT FTM STL',\n",
       " 'FG3_PCT FTM BLK',\n",
       " 'FG3_PCT FTM TOV',\n",
       " 'FG3_PCT FTM PF',\n",
       " 'FG3_PCT FTM PTS',\n",
       " 'FG3_PCT FTA^2',\n",
       " 'FG3_PCT FTA FT_PCT',\n",
       " 'FG3_PCT FTA OREB',\n",
       " 'FG3_PCT FTA DREB',\n",
       " 'FG3_PCT FTA REB',\n",
       " 'FG3_PCT FTA AST',\n",
       " 'FG3_PCT FTA STL',\n",
       " 'FG3_PCT FTA BLK',\n",
       " 'FG3_PCT FTA TOV',\n",
       " 'FG3_PCT FTA PF',\n",
       " 'FG3_PCT FTA PTS',\n",
       " 'FG3_PCT FT_PCT^2',\n",
       " 'FG3_PCT FT_PCT OREB',\n",
       " 'FG3_PCT FT_PCT DREB',\n",
       " 'FG3_PCT FT_PCT REB',\n",
       " 'FG3_PCT FT_PCT AST',\n",
       " 'FG3_PCT FT_PCT STL',\n",
       " 'FG3_PCT FT_PCT BLK',\n",
       " 'FG3_PCT FT_PCT TOV',\n",
       " 'FG3_PCT FT_PCT PF',\n",
       " 'FG3_PCT FT_PCT PTS',\n",
       " 'FG3_PCT OREB^2',\n",
       " 'FG3_PCT OREB DREB',\n",
       " 'FG3_PCT OREB REB',\n",
       " 'FG3_PCT OREB AST',\n",
       " 'FG3_PCT OREB STL',\n",
       " 'FG3_PCT OREB BLK',\n",
       " 'FG3_PCT OREB TOV',\n",
       " 'FG3_PCT OREB PF',\n",
       " 'FG3_PCT OREB PTS',\n",
       " 'FG3_PCT DREB^2',\n",
       " 'FG3_PCT DREB REB',\n",
       " 'FG3_PCT DREB AST',\n",
       " 'FG3_PCT DREB STL',\n",
       " 'FG3_PCT DREB BLK',\n",
       " 'FG3_PCT DREB TOV',\n",
       " 'FG3_PCT DREB PF',\n",
       " 'FG3_PCT DREB PTS',\n",
       " 'FG3_PCT REB^2',\n",
       " 'FG3_PCT REB AST',\n",
       " 'FG3_PCT REB STL',\n",
       " 'FG3_PCT REB BLK',\n",
       " 'FG3_PCT REB TOV',\n",
       " 'FG3_PCT REB PF',\n",
       " 'FG3_PCT REB PTS',\n",
       " 'FG3_PCT AST^2',\n",
       " 'FG3_PCT AST STL',\n",
       " 'FG3_PCT AST BLK',\n",
       " 'FG3_PCT AST TOV',\n",
       " 'FG3_PCT AST PF',\n",
       " 'FG3_PCT AST PTS',\n",
       " 'FG3_PCT STL^2',\n",
       " 'FG3_PCT STL BLK',\n",
       " 'FG3_PCT STL TOV',\n",
       " 'FG3_PCT STL PF',\n",
       " 'FG3_PCT STL PTS',\n",
       " 'FG3_PCT BLK^2',\n",
       " 'FG3_PCT BLK TOV',\n",
       " 'FG3_PCT BLK PF',\n",
       " 'FG3_PCT BLK PTS',\n",
       " 'FG3_PCT TOV^2',\n",
       " 'FG3_PCT TOV PF',\n",
       " 'FG3_PCT TOV PTS',\n",
       " 'FG3_PCT PF^2',\n",
       " 'FG3_PCT PF PTS',\n",
       " 'FG3_PCT PTS^2',\n",
       " 'FTM^3',\n",
       " 'FTM^2 FTA',\n",
       " 'FTM^2 FT_PCT',\n",
       " 'FTM^2 OREB',\n",
       " 'FTM^2 DREB',\n",
       " 'FTM^2 REB',\n",
       " 'FTM^2 AST',\n",
       " 'FTM^2 STL',\n",
       " 'FTM^2 BLK',\n",
       " 'FTM^2 TOV',\n",
       " 'FTM^2 PF',\n",
       " 'FTM^2 PTS',\n",
       " 'FTM FTA^2',\n",
       " 'FTM FTA FT_PCT',\n",
       " 'FTM FTA OREB',\n",
       " 'FTM FTA DREB',\n",
       " 'FTM FTA REB',\n",
       " 'FTM FTA AST',\n",
       " 'FTM FTA STL',\n",
       " 'FTM FTA BLK',\n",
       " 'FTM FTA TOV',\n",
       " 'FTM FTA PF',\n",
       " 'FTM FTA PTS',\n",
       " 'FTM FT_PCT^2',\n",
       " 'FTM FT_PCT OREB',\n",
       " 'FTM FT_PCT DREB',\n",
       " 'FTM FT_PCT REB',\n",
       " 'FTM FT_PCT AST',\n",
       " 'FTM FT_PCT STL',\n",
       " 'FTM FT_PCT BLK',\n",
       " 'FTM FT_PCT TOV',\n",
       " 'FTM FT_PCT PF',\n",
       " 'FTM FT_PCT PTS',\n",
       " 'FTM OREB^2',\n",
       " ...]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pf = PolynomialFeatures(degree=3)\n",
    "pf.fit(df_train[p1_features])\n",
    "feature_names = pf.get_feature_names(p1_features)\n",
    "feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>FGM</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>FGA</td>\n",
       "      <td>-0.256749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>FG_PCT</td>\n",
       "      <td>0.595982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>FG3M</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>FG3A</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>FG3_PCT</td>\n",
       "      <td>0.278660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>FTM</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>FTA</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>FT_PCT</td>\n",
       "      <td>0.000000</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      name    weight\n",
       "0        1  0.000000\n",
       "1      FGM  0.000000\n",
       "2      FGA -0.256749\n",
       "3   FG_PCT  0.595982\n",
       "4     FG3M  0.000000\n",
       "5     FG3A  0.000000\n",
       "6  FG3_PCT  0.278660\n",
       "7      FTM  0.000000\n",
       "8      FTA  0.000000\n",
       "9   FT_PCT  0.000000"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_table = pd.DataFrame({\n",
    "    'name': feature_names,\n",
    "    'weight': p1f_model.named_steps[\"model\"].coef_[0]\n",
    "})\n",
    "feature_table.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>REB</td>\n",
       "      <td>1.334164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>FG_PCT</td>\n",
       "      <td>0.595982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>STL</td>\n",
       "      <td>0.321964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>FG3_PCT</td>\n",
       "      <td>0.278660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>529</th>\n",
       "      <td>FG_PCT^2 PTS</td>\n",
       "      <td>0.173999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>FGA REB TOV</td>\n",
       "      <td>-0.099364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>DREB BLK</td>\n",
       "      <td>-0.100161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>885</th>\n",
       "      <td>FG3_PCT^2 TOV</td>\n",
       "      <td>-0.101834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>FGA</td>\n",
       "      <td>-0.256749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>TOV</td>\n",
       "      <td>-0.428387</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              name    weight\n",
       "12             REB  1.334164\n",
       "3           FG_PCT  0.595982\n",
       "14             STL  0.321964\n",
       "6          FG3_PCT  0.278660\n",
       "529   FG_PCT^2 PTS  0.173999\n",
       "..             ...       ...\n",
       "490    FGA REB TOV -0.099364\n",
       "158       DREB BLK -0.100161\n",
       "885  FG3_PCT^2 TOV -0.101834\n",
       "2              FGA -0.256749\n",
       "16             TOV -0.428387\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_table[abs(feature_table['weight']) > 10**-2].sort_values(\n",
    "    'weight', ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: Logistic Regression from Scratch (Optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below fits an sklearn `LogisticRegression` model with `C = 1e-2` to the NBA dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=0.001, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2_features = ['FGM', 'FGA', 'STL']\n",
    "p2_sklearn_model = LogisticRegression(C=1e-3)\n",
    "p2_sklearn_model.fit(df_train[p2_features], df_train[\"WON\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.20493073])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2_sklearn_model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.19994998, -0.07420132,  0.08193321]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2_sklearn_model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using this model, we can predict the chance that a team will win if it attempts 50 field goals, succeeds at 30 of them, and also performs 20 steals. In this case, the model predicts this team will win with approximately 84.8% probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.15159227, 0.84840773]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2_sklearn_model.predict_proba([[30, 50, 20]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also make multiple predictions at once, i.e. below we see that a team that makes 0 out of 0 field goal attempts and also makes 0 steals is predicted to win with an approximately 9.9% chance by our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.15159227, 0.84840773],\n",
       "       [0.90069142, 0.09930858]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2_sklearn_model.predict_proba([[30, 50, 20], [0, 0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In problem 1, we saw how to fit such models. In this problem, we'll explore how the `LogisticRegression` class really works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P1A: Understanding `predict_proba`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, implement the `my_predict_proba` function.\n",
    "\n",
    "This function should return the chance that each of the given teams wins the game as a function of intercept and coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_predict_proba(intercept, coef, X):\n",
    "\n",
    "    def sigma(x_):\n",
    "        return 1 / (1 + np.exp(-x_))\n",
    "\n",
    "    return sigma(intercept + np.sum(coef * X, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, when running the code below, you should get back `[0.848, 0.0933]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.84840773, 0.09930858])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1a_intercept = -2.20493073\n",
    "p1a_coef = np.array([0.19994998, -0.07420132, 0.08193321])\n",
    "p1a_X = np.array([[30, 50, 20], [0, 0, 0]])\n",
    "my_predict_proba(p1a_intercept, p1a_coef, p1a_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2B: Cross Entropy Loss Review"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that we have two basketball games:\n",
    "1. Team A makes 30 out of 50 field goals, and steals the ball 20 times. Team A wins.\n",
    "2. Team A makes 0 out of 0 field goals, and steals the ball 0 times. Team A loses.\n",
    "\n",
    "Write code below that computes the **total** cross-entropy loss of our model above on the given data. You can either do this by implementing the cross-entropy loss function yourself, or by using the sklearn `log_loss` function.\n",
    "\n",
    "**Hint:** If you set the parameter `normalize = False` in the sklearn `log_loss` function, you will get the total cross-entropy loss. \n",
    "\n",
    "You should get a value around 0.269."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.26898651122694023"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss([1, 0], [0.84840773, 0.09930858], normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2C: Implementing `p2c_total_cross_entropy_loss`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, define a function `p2c_total_cross_entropy_loss` that gives the cross entropy loss of the model with given `coef` and `intercept` applied to the given `X` and `y` data.\n",
    "\n",
    "**Hint:** You'll need to use the `my_predict_proba` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def p2c_total_cross_entropy_loss(y, intercept, coef, X):\n",
    "    return log_loss(y, my_predict_proba(intercept, coef, X), normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below should give the same answer as you computed in `P2B`. In other words, it should be approximatley 0.269."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2689865094750521"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2c_total_cross_entropy_loss([1, 0], p1a_intercept, p1a_coef, p1a_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we can compute the total cross entropy loss of the same model on the entire NBA dataset. You should get around 1,158."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1158.0808948850881"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2c_total_cross_entropy_loss(df_train[\"WON\"], p1a_intercept, p1a_coef,\n",
    "                             df_train[p2_features])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2D: Getting a Better Fit Manually"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try changing the intercept and coefficients provided as parameters to the function below. Observe what happens to the total cross entropy loss.\n",
    "\n",
    "Most likely, if you change any values, you'll get slightly worse results. This is because the intercept and coefficients that we are using have been generated by sklearn to be optimal for this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1158.0808948850881"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2c_total_cross_entropy_loss(df_train[\"WON\"], -2.20493073,\n",
    "                             np.array([[0.19994998, -0.07420132, 0.08193321]]),\n",
    "                             df_train[p2_features])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2E: Understanding `minimize`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the function `x^4 - 4*x^3 + 2*x^2 + x + 1`. The minimum of this function can be seen visually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2, 4, 100)\n",
    "\n",
    "\n",
    "def f_example_1D(x):\n",
    "    return x**4 - 4 * x**3 + 2 * x**2 + x + 1\n",
    "\n",
    "\n",
    "plt.plot(x, f_example_1D(x))\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `minimize` function of sklearn is able to find the minima of arbitrary functions. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: -7.494017550907326\n",
       " hess_inv: array([[0.04601209]])\n",
       "      jac: array([5.96046448e-07])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 21\n",
       "      nit: 5\n",
       "     njev: 7\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([2.57371512])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "minimize(f_example_1D, x0=[1.3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code above tells us that the minimizing x is 2.57. We can extract this optimal value by asking for the 'x' from the above dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.57371512]\n"
     ]
    }
   ],
   "source": [
    "best_x = minimize(f_example_1D, x0=[1.3])['x']\n",
    "print(best_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `x0` we provide to minimize tells the scipy optimizer where to start looking for an optimum. That is, we can think of our algorithm as starting at the red dot and eventually ending up at the minimum at the blue dot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2, 4, 100)\n",
    "\n",
    "\n",
    "def f_example_1D(x):\n",
    "    return x**4 - 4 * x**3 + 2 * x**2 + x + 1\n",
    "\n",
    "\n",
    "plt.plot(x, f_example_1D(x))\n",
    "plt.plot(1.3, f_example_1D(1.3), 'ro', markersize=12)\n",
    "plt.plot(2.57, f_example_1D(2.57), 'bo', markersize=12)\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Technical Note:** For general functions, the starting point we select can affect the final outcome. However, the cross entropy loss we'll be using later in this problem has a special property called \"convexity\" where the starting point we select does not matter. This is beyond the scope of our class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use `optimize` to minimize multi-dimensional functions. For example, consider the function (1 - x)^2 + 100(y - x^2 + 2)^2, which you can see visualized below or at [this link](https://en.wikipedia.org/wiki/Rosenbrock_function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "\n",
    "def f(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    return (1 - x)**2 + 100 * (y - x**2 + 2)**2\n",
    "\n",
    "\n",
    "X = np.linspace(-2, 2, 50)\n",
    "Y = np.linspace(-2, 2, 50)\n",
    "\n",
    "p = np.meshgrid(X, Y)\n",
    "Z = f(p)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z')\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function is smallest in the large flat light colored region. Let's see what happens when we use scipy optimize on this function. We'll start at x = 0, y = 2, which is at the top of the black hill."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 2.5830924248898155e-11\n",
       " hess_inv: array([[0.52024305, 1.0407402 ],\n",
       "       [1.0407402 , 2.08699126]])\n",
       "      jac: array([ 1.74013243e-06, -1.47256660e-06])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 148\n",
       "      nit: 25\n",
       "     njev: 37\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([ 0.99999492, -1.00001018])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(f, x0=[0, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, we see the optimal input is approximately x = 1, y = -1. We can again plot this result as a starting red dot and a final blue dot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "\n",
    "def f(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    return (1 - x)**2 + 100 * (y - x**2 + 2)**2\n",
    "\n",
    "\n",
    "X = np.linspace(-2, 2, 50)\n",
    "Y = np.linspace(-2, 2, 50)\n",
    "\n",
    "p = np.meshgrid(X, Y)\n",
    "Z = f(p)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
    "ax.scatter(0, 2, 1600, c='r', s=500)\n",
    "ax.scatter(1, -1, 0, c='b', s=500)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z')\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it's your turn. As an exercise, use scipy's `minimize` to find the minimum of $$x^2 + \\frac{y^2}{3} + z^2 + 2x + 5y + 1$$\n",
    "\n",
    "You should get x = -1, y = -1.5, z = 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: -18.749999999999993\n",
       " hess_inv: array([[ 5.01235319e-01, -1.63578381e-04, -3.77325322e-07],\n",
       "       [-1.63578381e-04,  1.49997451e+00,  7.74273572e-08],\n",
       "       [-3.77325322e-07,  7.74273572e-08,  1.00000000e+00]])\n",
       "      jac: array([0., 0., 0.])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 40\n",
       "      nit: 7\n",
       "     njev: 8\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([-9.99999940e-01, -7.49999991e+00, -4.23612610e-09])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f3(p):\n",
    "    x = p[0]\n",
    "    y = p[1]\n",
    "    z = p[2]\n",
    "    return x**2 + y**2 / 3 + z**2 + 2 * x + 5 * y + 1\n",
    "\n",
    "\n",
    "minimize(f3, x0=[0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2F: Fitting the model (Hard Problem!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `minimize` to find `intercept` and `coef` that minimize training error.\n",
    "\n",
    "**Hint:** Define a function `total_nba_cross_entropy_training_loss(thetas)` that gives the total cross entropy loss on the training set as a function of the intercept and coefficients. \n",
    "\n",
    "**Hint:** Your `p2c_total_cross_entropy_loss` problem will be useful here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your code shield give approximately intercept = `-2.44` and coefficients = `0.24, -0.09,  0.11`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def total_nba_cross_entropy_training_loss(thetas):\n",
    "    return p2c_total_cross_entropy_loss(df_train[\"WON\"], thetas[0], thetas[1:],\n",
    "                                        df_train[p2_features])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 1152.4620232776037\n",
       " hess_inv: array([[ 5.53741993e-05, -1.30081753e-06, -3.43206921e-08,\n",
       "         9.22606887e-07],\n",
       "       [-1.30081753e-06,  2.90285366e-04, -1.31537035e-04,\n",
       "        -1.18058227e-04],\n",
       "       [-3.43206921e-08, -1.31537035e-04,  6.18978491e-05,\n",
       "         2.66145793e-05],\n",
       "       [ 9.22606887e-07, -1.18058227e-04,  2.66145793e-05,\n",
       "         4.40859372e-04]])\n",
       "      jac: array([-0.00028992, -0.01107788, -0.02577209, -0.00268555])\n",
       "  message: 'Desired error not necessarily achieved due to precision loss.'\n",
       "     nfev: 139\n",
       "      nit: 12\n",
       "     njev: 23\n",
       "   status: 2\n",
       "  success: False\n",
       "        x: array([-2.43815461,  0.23876416, -0.09202757,  0.1122991 ])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(total_nba_cross_entropy_training_loss, x0=[0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intercept and theta we got above are not the same as we used earlier in the problem. For example, your code from P2E found that the coefficient for `FGA` is 0.24, but the example I gave at the beginning of this problem was 0.2.\n",
    "\n",
    "The reason is that the coefficient we computed at the beginning of this problem was from a regularized model where `C=1e-3`.\n",
    "\n",
    "Below, we create a `LogisticRegression` object with `penalty = 'none'` and fit it to the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='none',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model = LogisticRegression(penalty='none')\n",
    "p2f_model.fit(df_train[p2_features], df_train[\"WON\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe below that the `intercept_` and `coef_` and they should be very close to the intercept and coefficients that you computed earlier in `P2E`.\n",
    "\n",
    "This is great! It means that what you just did in `P2E` is implement your very own logistic regression model. Good job!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.43824694])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.23876388, -0.09202659,  0.11230134]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2G: Fitting a Regularized Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In P2E, you found the $\\theta$ values that minimized the total cross entropy loss (TCEL). Or in otherwords, you minimized:\n",
    "\n",
    "$$\\sum_{i = 1}^n -\\ln(1-\\Delta y_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function that sklearn minimizes when regularizing is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{1}{2C} \\sum_{i = 2}^d \\theta_i^2 + \\sum_{i = 1}^n -\\ln(1-\\Delta y_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we assume the intercept is $\\theta_1$, so it is not included in the left sum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, use `minimize` to compute the $\\theta$ values that minimize the sum above.\n",
    "\n",
    "You should get the same $\\theta$ we used at the beginning of Problem 2, i.e. intercept = -2.2, and coefficients = 0.2, -0.07, and 0.08.\n",
    "\n",
    "Once you've done this, you've shown that you've essentially implemented your own `fit` function. Good job! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "def total_nba_cross_entropy_training_loss_plus_regularization(thetas):\n",
    "    loss = p2c_total_cross_entropy_loss(df_train['WON'], thetas[0], thetas[1:],\n",
    "                                        df_train[p2_features])\n",
    "    weight = 1 / 2e-3 * np.sum(thetas[1:]**2)\n",
    "    return loss + weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 1184.1803355448894\n",
       " hess_inv: array([[ 6.20880656e-04, -2.63324399e-04,  1.16110834e-04,\n",
       "        -1.80957928e-05],\n",
       "       [-2.63324399e-04,  1.31204336e-04, -5.83460886e-05,\n",
       "         8.87495782e-06],\n",
       "       [ 1.16110834e-04, -5.83460886e-05,  2.76699171e-05,\n",
       "        -2.06517975e-05],\n",
       "       [-1.80957928e-05,  8.87495782e-06, -2.06517975e-05,\n",
       "         1.97945588e-04]])\n",
       "      jac: array([-3.05175781e-05, -9.30786133e-04, -2.70080566e-03, -1.98364258e-04])\n",
       "  message: 'Desired error not necessarily achieved due to precision loss.'\n",
       "     nfev: 127\n",
       "      nit: 12\n",
       "     njev: 21\n",
       "   status: 2\n",
       "  success: False\n",
       "        x: array([-2.20484264,  0.19995038, -0.07420251,  0.08193344])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(total_nba_cross_entropy_training_loss_plus_regularization,\n",
    "         x0=[0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P2H: Bonus Exercise: Building Your Own LogisticRegression Class (hard)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given what you learned in the previous parts of this problem, implement the `MyLogisticRegression` class below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyLogisticRegression(object):\n",
    "\n",
    "    def __init__(self, C=1.0):\n",
    "        self.C = C\n",
    "\n",
    "    def fit(self, X, y):\n",
    "\n",
    "        def log_loss_function_plus_penalty(thetas):\n",
    "            model = MyLogisticRegression()\n",
    "            model.intercept_ = thetas[0]\n",
    "            model.coef_ = thetas[1:]\n",
    "            return log_loss(\n",
    "                y, model.predict_proba(X),\n",
    "                normalize=False) + 1.0 / (2 * self.C) * np.sum(thetas[1:]**2)\n",
    "\n",
    "        params = minimize(log_loss_function_plus_penalty,\n",
    "                          x0=np.zeros(X.shape[1] + 1))['x']\n",
    "        self.intercept_ = params[0]\n",
    "        self.coef_ = params[1:]\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        \"\"\"return 1D array equal to probability that X belongs to class 1\"\"\"\n",
    "\n",
    "        def sigma(x):\n",
    "            return 1 / (1 + np.exp(-x))\n",
    "\n",
    "        return sigma(np.sum(self.coef_ * X, 1) + self.intercept_)\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\"returns 1D array of predictions for X\"\"\"\n",
    "        return (self.predict_proba(X) > 0.5).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "p2f_model = MyLogisticRegression(C=1e-3)\n",
    "p2f_model.fit(df_train[p2_features], df_train[\"WON\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intercept should be -2.2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.2048426368444547"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coefficients should be 0.2, -0.07, 0.08/."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.19995038, -0.07420251,  0.08193344])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predictions should be 0.85, 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.84841353, 0.09931646])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2f_model.predict_proba([[30, 50, 20], [0, 0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Optional Part 3: Intercept Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This part of the homework is less important, but some of you might find it interesitng."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "titanic_df = sns.load_dataset(\"titanic\")\n",
    "titanic_df = titanic_df[[\"age\", \"fare\", \"pclass\", \"sex\", \"survived\"]].copy()\n",
    "titanic_df = titanic_df.dropna()\n",
    "titanic_df['sex'] = titanic_df['sex'].replace(\"male\", 0)\n",
    "titanic_df['sex'] = titanic_df['sex'].replace(\"female\", 1)\n",
    "np.random.seed(23)\n",
    "titanic_train, titanic_test = np.split(titanic_df, [600])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we have trained two models on the titanic dataset.\n",
    "\n",
    "As described in lecture, `tiny_c_model_fit_intercept_true` has two intercepts, one of which is regularized, and one of which is unregularized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "tiny_c_model_fit_intercept_true = Pipeline([\n",
    "    ('scale', StandardScaler()), ('poly', PolynomialFeatures(degree=2)),\n",
    "    ('model', LogisticRegression(fit_intercept=True, C=1e-8))\n",
    "])\n",
    "tiny_c_model_fit_intercept_true.fit(\n",
    "    titanic_train[[\"fare\", \"age\", \"pclass\", \"sex\"]], titanic_train[\"survived\"])\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that one of the intercepts is around 10^-12. This is 0th entry of the `coef_`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.25694801e-12,  7.51227164e-07, -2.65119113e-07,\n",
       "        -1.03238354e-06,  1.56658189e-06,  2.11003830e-06,\n",
       "         1.57498539e-07, -6.45345674e-07,  2.85642088e-07,\n",
       "         2.51417259e-08,  8.11665626e-08,  9.48429057e-08,\n",
       "         3.59262878e-07, -4.70406297e-07,  8.90303584e-07]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_true.named_steps[\"model\"].coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the other is around -0.377. This is the unregularized intercept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.3777663])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_true.named_steps[\"model\"].intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By contrast, if we set `fit_intercept = False`, the resulting `intercept_` is zero, and we're left with only the regularized intercept given by the 0th entry of `coef_`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "tiny_c_model_fit_intercept_false = Pipeline([\n",
    "    ('scale', StandardScaler()), ('poly', PolynomialFeatures(degree=2)),\n",
    "    ('model', LogisticRegression(fit_intercept=False, C=1e-8))\n",
    "])\n",
    "tiny_c_model_fit_intercept_false.fit(\n",
    "    titanic_train[[\"fare\", \"age\", \"pclass\", \"sex\"]], titanic_train[\"survived\"])\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.60001095e-07,  7.51233457e-07, -2.65119073e-07,\n",
       "        -1.03238765e-06,  1.56658614e-06,  1.55006743e-06,\n",
       "         1.14122444e-07, -3.34537258e-07,  1.91154249e-07,\n",
       "        -5.34859749e-07,  2.87975816e-07,  1.77232437e-07,\n",
       "        -2.00738071e-07, -3.98849755e-07,  3.30302647e-07]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_false.named_steps[\"model\"].coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_false.named_steps[\"model\"].intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P3A: Accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the `tiny_c_model_fit_intercept_true` has more freedom to pick a better intercept, you might expect that it should have higher accuracy. Let's test this hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the accuracy of our two models using sklearn's `accuracy_score` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5964912280701754"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_fit_intercept_true = accuracy_score(\n",
    "    titanic_test[\"survived\"],\n",
    "    tiny_c_model_fit_intercept_true.predict(\n",
    "        titanic_test[[\"fare\", \"age\", \"pclass\", \"sex\"]]))\n",
    "accuracy_fit_intercept_true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7807017543859649"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_fit_intercept_false = accuracy_score(\n",
    "    titanic_test[\"survived\"],\n",
    "    tiny_c_model_fit_intercept_false.predict(\n",
    "        titanic_test[[\"fare\", \"age\", \"pclass\", \"sex\"]]))\n",
    "accuracy_fit_intercept_false"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should see that surprisingly, the model with the `fit_intercept = False` actually has higher accuracy! Over the next few problems, we'll see why."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P3B: Cross Entropy "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, compute the **total** cross entropy loss for the two models. You should see that `tiny_c_model_fit_intercept_true` is better than `tiny_c_model_fit_intercept_false`, i.e. the log_loss is lower for the model that pick its intercept without worrying about regularization. \n",
    "\n",
    "You should get approximately 405 for `tiny_c_model_fit_intercept_true` and 416 for `tiny_c_model_fit_intercept_false`.\n",
    "\n",
    "Reminder; Make sure to set `normalize = False` when calling `log_loss`. This gives you back the total cross entropy loss instead of the average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "415.887534194071"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss(titanic_train['survived'],\n",
    "         tiny_c_model_fit_intercept_false.predict_proba(\n",
    "             titanic_train[['fare', 'age', 'pclass', 'sex']]),\n",
    "         normalize=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "405.3723770626674"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss(titanic_train['survived'],\n",
    "         tiny_c_model_fit_intercept_true.predict_proba(\n",
    "             titanic_train[['fare', 'age', 'pclass', 'sex']]),\n",
    "         normalize=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "79.01867046324062"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss(titanic_test['survived'],\n",
    "         tiny_c_model_fit_intercept_false.predict_proba(\n",
    "             titanic_test[['fare', 'age', 'pclass', 'sex']]),\n",
    "         normalize=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "76.88480869635879"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss(titanic_test['survived'],\n",
    "         tiny_c_model_fit_intercept_true.predict_proba(\n",
    "             titanic_test[['fare', 'age', 'pclass', 'sex']]),\n",
    "         normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our observations are summarized in the table below.\n",
    "\n",
    "|                       | accuracy | cross entropy loss |\n",
    "|-----------------------|----------|--------------------|\n",
    "| `fit_intercept = True`  | 59%      | 405                |\n",
    "| `fit_intercept = False` | 77%      | 416                |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is better? It depends on how you define better.\n",
    "\n",
    "The LogisticRegression model defines \"better\" as lower cross-entropy loss. From that perspective, `fit_intercept = True` is bettre, since cross entropy loss is only 405.\n",
    "\n",
    "However, as a human using the model, you might care more about accuracy. Or perhaps you care about another measure like \"true positive rate\". We will discuss other such measurements in a future lecture.\n",
    "\n",
    "**Note: The REAL problem here is that we have picked a C which is much too small (C = 1e-8). This results in a model that is vastly underfit and cannot perform well on the provided data.** In real world scenarios with reasonable hyperparameter choices, it is uncommon for accuracy and cross entropy loss to be so out of sync."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### P3C: A Closer Look"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might find it interesting to see the output of our two models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.59333429, 0.40666571],\n",
       "       [0.59333212, 0.40666788],\n",
       "       [0.59333359, 0.40666641],\n",
       "       ...,\n",
       "       [0.5933332 , 0.4066668 ],\n",
       "       [0.59333424, 0.40666576],\n",
       "       [0.59333438, 0.40666562]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_true.predict_proba(\n",
    "    titanic_train[[\"fare\", \"age\", \"pclass\", \"sex\"]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.50000055, 0.49999945],\n",
       "       [0.49999872, 0.50000128],\n",
       "       [0.49999989, 0.50000011],\n",
       "       ...,\n",
       "       [0.49999979, 0.50000021],\n",
       "       [0.50000085, 0.49999915],\n",
       "       [0.50000056, 0.49999944]])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tiny_c_model_fit_intercept_false.predict_proba(\n",
    "    titanic_train[[\"fare\", \"age\", \"pclass\", \"sex\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we see is that the `fit_intercept_true` model basically just gives every passenger a 40.6% chance of surviving. This is also the fraction of passengers who survived. That means that the class it predicts for every passenger is 0, i.e. it thinks everyone died. This is why the accuracy is relatively poor, since it gets every single surviving passenger wrong.\n",
    "\n",
    "By contrast, `fit_intercept_false` gives every passenger an approximately 50% chance of surviving. In this case, the classes for passengers are 0 or 1, resulting in an overall 77% accuracy."
   ]
  }
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